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Confidence intervals for long-horizon predictive regressions via reverse regressions

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  • Min Wei
  • Jonathan H. Wright

Abstract

Long-horizon predictive regressions in finance pose formidable econometric problems when estimated using the sample sizes that are typically available. A remedy that has been proposed by Hodrick (1992) is to run a reverse regression in which short-horizon returns are projected onto a long-run mean of some predictor. By covariance stationarity, the slope coefficient is zero in the reverse regression if and only if it is zero in the original regression, but testing the hypothesis in the reverse regression avoids small sample problems. Unfortunately this only allows us to test the null of no predictability. In this paper we show how to use the reverse regression to test other hypotheses about the slope coefficient in a long-horizon predictive regression, and to form confidence intervals for this coefficient. We show that this approach to inference works well in small samples.

Suggested Citation

  • Min Wei & Jonathan H. Wright, 2009. "Confidence intervals for long-horizon predictive regressions via reverse regressions," Finance and Economics Discussion Series 2009-27, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2009-27
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-853, October.
    2. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 459-491, December.
    3. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-679, June.
    4. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    5. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    6. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    7. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 2001. "Peso problem explanations for term structure anomalies," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 241-270, October.
    8. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
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    Cited by:

    1. Bakshi, Gurdip & Panayotov, George, 2013. "Predictability of currency carry trades and asset pricing implications," Journal of Financial Economics, Elsevier, vol. 110(1), pages 139-163.
    2. Bakshi, Gurdip & Panayotov, George & Skoulakis, Georgios, 2011. "Improving the predictability of real economic activity and asset returns with forward variances inferred from option portfolios," Journal of Financial Economics, Elsevier, vol. 100(3), pages 475-495, June.
    3. Heaton, Chris, 2015. "Testing for multiple-period predictability between serially dependent time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 587-597.

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    Keywords

    Regression analysis ; Stocks;

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